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Examples
========

Below are examples illustrating Simcoon's main features. 
These examples are designed to serve as tutorials. 
In that sense, an effort is made to keep the scripts simple and executable with 
a low computational cost.



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Analysis and processing examples
-----------------------------------

Below are examples illustrating Simcoon's capabilities for simulating mechanical and thermomechanical
responses and post-processing results.


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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial studies the directional stiffness of a cubic material">

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  .. image:: /examples/analysis/images/thumb/sphx_glr_directional_stiffness_thumb.png
    :alt:

  :doc:`/examples/analysis/directional_stiffness`

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      <div class="sphx-glr-thumbnail-title">Effective properties of a cubic material</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Numerical vs Analytical Eshelby Tensor Comparison">

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  .. image:: /examples/analysis/images/thumb/sphx_glr_eshelby_numerical_vs_analytical_thumb.png
    :alt:

  :doc:`/examples/analysis/eshelby_numerical_vs_analytical`

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      <div class="sphx-glr-thumbnail-title">Numerical vs Analytical Eshelby Tensor Comparison</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Comparison of objective rates">

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  .. image:: /examples/analysis/images/thumb/sphx_glr_objective_rates_thumb.png
    :alt:

  :doc:`/examples/analysis/objective_rates`

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      <div class="sphx-glr-thumbnail-title">Comparison of objective rates</div>
    </div>


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.. toctree::
   :hidden:

   /examples/analysis/directional_stiffness
   /examples/analysis/eshelby_numerical_vs_analytical
   /examples/analysis/objective_rates

Continuum Mechanics Examples
-----------------------------------------------

Below are examples illustrating Simcoon's main features. 
These examples are designed to serve as tutorials. 
In that sense, an effort is made to keep the scripts simple and executable with 
a low computational cost.

This gallery contains examples demonstrating:

- **Constitutive relations** - Building stiffness and compliance tensors for various material symmetries
- **Stress measures** - Converting between different stress measures (Cauchy, PK1, PK2, etc.)
- **Rotation operations** - Rotating tensors and vectors
- **Yield criteria** - von Mises, Tresca, Drucker, and Hill anisotropic criteria



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  .. image:: /examples/continuum_mechanics/images/thumb/sphx_glr_constitutive_relations_thumb.png
    :alt:

  :doc:`/examples/continuum_mechanics/constitutive_relations`

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      <div class="sphx-glr-thumbnail-title">Constitutive Library Examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Rotation library Examples">

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  .. image:: /examples/continuum_mechanics/images/thumb/sphx_glr_rotation_thumb.png
    :alt:

  :doc:`/examples/continuum_mechanics/rotation`

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      <div class="sphx-glr-thumbnail-title">Rotation library Examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example is an hands-on demo of the stress “transfer” helpers in simcoon.simmit to switch between different stress measures.">

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  .. image:: /examples/continuum_mechanics/images/thumb/sphx_glr_stress_measures_thumb.png
    :alt:

  :doc:`/examples/continuum_mechanics/stress_measures`

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      <div class="sphx-glr-thumbnail-title">Stress transfer: Cauchy → PKI/PKII/Kirchhoff</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the stress transfer helpers exposed in simcoon.simmit.">

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  .. image:: /examples/continuum_mechanics/images/thumb/sphx_glr_stress_transfer_helpers_thumb.png
    :alt:

  :doc:`/examples/continuum_mechanics/stress_transfer_helpers`

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      <div class="sphx-glr-thumbnail-title">Stress transfer library examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates different yield criteria available in Simcoon, including von Mises, Tresca, Drucker, and anisotropic Hill criteria.">

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  .. image:: /examples/continuum_mechanics/images/thumb/sphx_glr_yield_criteria_thumb.png
    :alt:

  :doc:`/examples/continuum_mechanics/yield_criteria`

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      <div class="sphx-glr-thumbnail-title">Yield Criteria Examples</div>
    </div>


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.. toctree::
   :hidden:

   /examples/continuum_mechanics/constitutive_relations
   /examples/continuum_mechanics/rotation
   /examples/continuum_mechanics/stress_measures
   /examples/continuum_mechanics/stress_transfer_helpers
   /examples/continuum_mechanics/yield_criteria

Heterogeneous materials simulation
-----------------------------------------------

Below are examples illustrating Simcoon's capabilities for simulating heterogeneous materials.

This gallery contains examples demonstrating:

- **Eshelby tensors** - Computing Eshelby and Hill interaction tensors for various inclusion shapes
- **Micromechanics** - Effective properties using Mori-Tanaka and self-consistent schemes, effect of volume fraction and aspect ratio


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    <div class="sphx-glr-thumbcontainer" tooltip="This example studies the evolution of the mechanical properties of a composite material considering spherical reinforcement.">

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  .. image:: /examples/heterogeneous/images/thumb/sphx_glr_effective_props_thumb.png
    :alt:

  :doc:`/examples/heterogeneous/effective_props`

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      <div class="sphx-glr-thumbnail-title">Micromechanics Examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Eshelby Tensor Examples">

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  .. image:: /examples/heterogeneous/images/thumb/sphx_glr_eshelby_tensors_thumb.png
    :alt:

  :doc:`/examples/heterogeneous/eshelby_tensors`

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      <div class="sphx-glr-thumbnail-title">Eshelby Tensor Examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="2 phase composite homogenization example">

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  .. image:: /examples/heterogeneous/images/thumb/sphx_glr_homogenization_thumb.png
    :alt:

  :doc:`/examples/heterogeneous/homogenization`

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      <div class="sphx-glr-thumbnail-title">2 phase composite homogenization example</div>
    </div>


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.. toctree::
   :hidden:

   /examples/heterogeneous/effective_props
   /examples/heterogeneous/eshelby_tensors
   /examples/heterogeneous/homogenization

Hyperelasticity 
-----------------------------------------------

Below are examples illustrating Simcoon's capabilities for simulating materials exhibiting hyperelasticity.


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we compare three hyperelastic constitutive laws. Each model is run for uniaxial tension (UT), equibiaxial tension (ET), and pure shear (PS).">

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  .. image:: /examples/hyperelasticity/images/thumb/sphx_glr_HYPER_numerical_thumb.png
    :alt:

  :doc:`/examples/hyperelasticity/HYPER_numerical`

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      <div class="sphx-glr-thumbnail-title">Hyperelastic models - use the API</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we compare five hyperelastic constitutive laws. Each model is run for uniaxial tension (UT), equibiaxial tension (ET), and pure shear (PS).">

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  .. image:: /examples/hyperelasticity/images/thumb/sphx_glr_HYPER_umat_thumb.png
    :alt:

  :doc:`/examples/hyperelasticity/HYPER_umat`

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      <div class="sphx-glr-thumbnail-title">Hyperelastic models - use the umat</div>
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   /examples/hyperelasticity/HYPER_numerical
   /examples/hyperelasticity/HYPER_umat

Constitutive Laws Examples
-----------------------------------------------

Below are examples illustrating Simcoon's constitutive laws library.

This gallery contains examples demonstrating the following material models:

**Elastic Models:**

- **ELISO** - Isotropic elasticity
- **ELIST** - Transversely isotropic elasticity
- **ELORT** - Orthotropic elasticity

**Plasticity Models:**

- **EPICP** - Plasticity with isotropic hardening (power-law)
- **EPKCP** - Plasticity with combined isotropic and kinematic hardening
- **EPCHA** - Plasticity with Chaboche hardening (cyclic plasticity)


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  .. image:: /examples/umats/images/thumb/sphx_glr_ELISO_thumb.png
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  :doc:`/examples/umats/ELISO`

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      <div class="sphx-glr-thumbnail-title">Isotropic elasticity examples</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Transversely Isotropic Elasticity Example">

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  .. image:: /examples/umats/images/thumb/sphx_glr_ELIST_thumb.png
    :alt:

  :doc:`/examples/umats/ELIST`

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      <div class="sphx-glr-thumbnail-title">Transversely Isotropic Elasticity Example</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Orthotropic Elasticity Example">

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  .. image:: /examples/umats/images/thumb/sphx_glr_ELORT_thumb.png
    :alt:

  :doc:`/examples/umats/ELORT`

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      <div class="sphx-glr-thumbnail-title">Orthotropic Elasticity Example</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Plasticity with Chaboche Hardening Example">

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  .. image:: /examples/umats/images/thumb/sphx_glr_EPCHA_thumb.png
    :alt:

  :doc:`/examples/umats/EPCHA`

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      <div class="sphx-glr-thumbnail-title">Plasticity with Chaboche Hardening Example</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Plasticity with isotropic hardening example">

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  .. image:: /examples/umats/images/thumb/sphx_glr_EPICP_thumb.png
    :alt:

  :doc:`/examples/umats/EPICP`

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      <div class="sphx-glr-thumbnail-title">Plasticity with isotropic hardening example</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Plasticity with Isotropic and Kinematic Hardening Example">

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  .. image:: /examples/umats/images/thumb/sphx_glr_EPKCP_thumb.png
    :alt:

  :doc:`/examples/umats/EPKCP`

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      <div class="sphx-glr-thumbnail-title">Plasticity with Isotropic and Kinematic Hardening Example</div>
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.. toctree::
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   /examples/umats/ELISO
   /examples/umats/ELIST
   /examples/umats/ELORT
   /examples/umats/EPCHA
   /examples/umats/EPICP
   /examples/umats/EPKCP


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      :download:`Download all examples in Python source code: examples_python.zip </examples/examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: examples_jupyter.zip </examples/examples_jupyter.zip>`


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    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_